UNIVERSITY OF VICTORIA MATH DIAGNOSTIC TEST

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UVIC MATH DIAGNOSTIC TEST PAGE 2 1. When the following numbers are listed from smallest to greatest: 2, 1.555, 14/9, 9/14, 9/13, 0.64, which is the fourth number in the list? (A) 2

(B) 1.555

(C) 14/9

(D) 9/14

(E) 9/13

(F) 0.64

This is a grade seven level question from the topic ”Fractions, Ratios and Proportions”. The correct choice is B. 2. Raja has been offered two jobs. Each of these jobs takes 24 weeks to complete. One job pays $3440 every 8 weeks. The other job pays $2700 every 6 weeks. Raja wants to accept the job that pays more per week. Which job should he pick? (A) The job that pays $3440 every 8 weeks. (B) The job that pays $2700 every 6 weeks. (C) Either of the two jobs, the pay is the same each week. This is a grade eight level question from the topic ”Fractions, Ratios and Proportions”. The correct choice is B. r 2 ? 3. Which interval(s) contains 7 (i) between 1/3 and 2/3 (ii) between 0pand 1/3 p (iii) between 5/21 and 9/21 (A) None (B) Only (i) (E) (i) and (ii) (F) (i) and (iii)

(C) Only (ii) (G) (ii) and (iii)

(D) Only (iii) (H) All

This is a grade nine level question from the topic ”Fractions, Ratios and Proportions”. The correct choice is F.

UVIC MATH DIAGNOSTIC TEST PAGE 3 4. Suppose that the volume of a right pyramid is 25cm3 and each side of the square base measures 3cm. What is the exact height of this pyramid in cm? Hint: the volume of a right pyramid is area of base × height/3. (A) 27 (B) 16 (C) 16/9 (F) 25/27 (G) 25/4 (H) 25/3

(D) 16/6 (I) 25

(E) 16/3 (J) none of the above

This is a grade ten level question from the topic ”Shape, Space and Geometry”. The correct choice is H. 5. A rectangular board has fallen across a set of railroad tracks (depicted below). Determine the measure of the angle θ in degrees. (A) 30 (F) 180

(B) 60 (G) 210

(C) 90 (H) 300

(D) 120 (I) 330

(E) 150 (J) none of the above

This is a basic grade eleven level question from the topic ”Shape, Space and Geometry”. The correct choice is E.

UVIC MATH DIAGNOSTIC TEST PAGE 4

6. Determine the exact value of x. √ (A) √2 (E) 4 2

(B) 2 (F) 8

√ (C) 2 √2 (G) 8 2

(D) 4 (H) none of the above

This is a grade ten level question from the topic ”Right Triangle Trigonometry”. The correct choice is C. 7. Determine the length of the fence shown below and select the appropriate expression. (A) 12 − 6 cos θ + 6 sin θ

(B) 12 + 6 cos θ − 6 sin θ

(C) 12 − 6 cos θ − 6 sin θ

(D) 12 −

6 6 + cos θ sin θ

(E) 12 +

6 6 − cos θ sin θ

(F) 12 −

6 6 − cos θ sin θ

(G) 12 −

6 6 + tan θ sin θ

(H) 12 +

6 6 − tan θ sin θ

(I) 12 −

6 6 − tan θ sin θ

(J) none of the above

This is a pre-calculus eleven level question from the topic ”Right Triangle Trigonometry”. The correct choice is G.

UVIC MATH DIAGNOSTIC TEST PAGE 5

 8. Simplify

− 2 27 3 . 8

(A) 65/24 (F) −272 /2

(B) −65/24 (G) 9/4

(E) 272 /2 (J) −4/9

(D) −64/3 (I) 4/9

(C) 64/3 (H) −9/4

This is a grade ten level question from the topic ”Exponents and Logarithms”. The correct choice is I. 9. Simplify (A) a3 b5 (E) a3 /b5

a−2 (a−1 b2 )3 (a3 b−1 )2 b3 (B) a3 b (F) a3 /b

(C) a−11 b5 (G) a−11 /b5

(D) a−11 b (H) a−11 /b

This is a grade ten level question from the topic ”Exponents and Logarithms”. The correct choice is C. 10. If log3 (x)√ = 5 and log3 (y) = 2 then which of the following equals log3 (y 3 · x)? (A) 10 (F) 8/5

√ (B) 8 5√ (G) 23 · 5

(C) 17/2√ (H) 6 + 5

(D) 15 √ (I) 23 + 5

(E) 16/5 (J) none of the above

This is a pre-calculus 12 level question from the topic ”Exponents and Logarithms”. The correct choice is C.

UVIC MATH DIAGNOSTIC TEST PAGE 6

11. Choose the inequality represented by the shaded area below. (A) y < x + 2 (E) y < −x + 2

(B) y ≤ x + 2 (F) x ≤ −y + 2

(C) x < y + 2 (D) x ≤ y + 2 (G) none of the above

This is a grade ten level question from the topic ”Lines, Polynomials and Factoring”. The correct choice is A. 12. What is the remainder when x3 + 3x2 + 5 is divided by x − 2? (A) 25x (E) 25

(B) −25x (F) −25

(C) −15x (G) −15

(D) −15x (H) −15

This is a pre-calculus 12 level question from the topic ”Lines, Polynomials and Factoring”. The correct choice is E.

UVIC MATH DIAGNOSTIC TEST PAGE 7

13. Given that the zeroes of a quadratic polynomial are −1 and −1/2 and the leading coefficient is 2, express the polynomial as a product of two binomials. (A) (x + 1)(x + 1/2) (D) (2x − 2)(x + 1/2) (G) (x − 1)(x − 1/2)

(B) (2x + 2)(x + 1/2) (E) (x + 1)(x − 1/2) (H) (2x − 2)(x − 1/2)

(C) (x − 1)(x + 1/2) (F) (2x + 2)(x − 1/2) (I) none of the above

This is a pre-calculus 12 level question from the topic ”Lines, Polynomials and Factoring”. The correct choice is B. 14. The fifth term in the geometric sequence 3, 6, ... is: (A) 15 (E) 37

(B) 20 (F) 42

(C) 26 (G) 48

(D) 31 (H) none of the above

This is a pre-calculus eleven level question from the topic ”Functions”. The correct choice is G. √ 15. If f (x) = x − 1 and g(x) = x2 then determine the domain of f (g(x)). (Note that for this question, the domain of a function is defined to be the largest set of real numbers for which the function is defined.) (A) all real numbers (D) only x ≤ 1 (G) x ≥ 0

(B) only x ≥ 1 (E) only x ≤ −1 (H) x > 0

(C) only x ≥ −1 (F) x ≤ −1 or x ≥ 1 (I) none of the above

This is a pre-calculus twelve level question from the topic ”Functions”. The correct choice is F.

UVIC MATH DIAGNOSTIC TEST PAGE 8

16. Determine the inverse function for the graph depicted below and express it in function notation. 5 (A) f (x) = x − 5 2

5 (B) f (x) = x + 5 2

5 (D) f (x) = − x + 5 2

(E) f (x) = 5x −

(G) f (x) = −5x −

5 2

5 (C) f (x) = − x − 5 2

5 2

(H) f (x) = −5x +

(F) f (x) = 5x + 5 2

5 2

(I) none of the above

This is a precalculus twelve level question from the topic ”Functions”. The correct choice is A.

UVIC MATH DIAGNOSTIC TEST PAGE 9

17. The graph of y = f (x) is depicted below. Which graph represents

y = 1/f (x)?

(A)

(B)

(C) This is a pre-calculus eleven level question from the topic ”Graphing Functions and Equations”. The correct choice is A.

UVIC MATH DIAGNOSTIC TEST PAGE 10

18. Find all solutions for the system: x + 2y = 5 and 7x + 9y = 6. (A) only x = 29/5, y = 33/5 (B) only x = 29/5, y = −33/5 (C) only x = 33/5, y = 29/5 (D) only x = −33/5, y = 29/5 (E) all points on the line y = 29/5 (F) all points on the line y = 33/5 (G) all points on the line y = −33/5 (H) all points on the line x = 29/5 (I) all points on the line x = 33/5 (J) all points on the line x = −33/5 This is a grade ten level question from the topic ”Solving Equations and Inequalities”. The correct choice is D. 19. Solve |x − 2| < 2 for x. (A) x < −4 (B) x ≤ −4 (C) −4 < x < 2 (E) −2 < x < 2 (F) −2 ≤ x ≤ 2 (G) 0 < x < 2 (I) 0 < x < 4 (J) 0 ≤ x ≤ 4

(D) −4 ≤ x ≤ 2 (H) 0 ≤ x ≤ 2

This is a pre-calculus eleven level question from the topic ”Solving Equations and Inequalities”. The correct choice is I. 20. Solve sin2 x+2sinx+1 = 0 for the exact value of x measured in radians where 0 ≤ x ≤ 2π. (A) x = π/2 (D) x = π

(B) x = 3π/2 (E) x = 5π/2

(C) x = 3π/4 (F) none of the above

This is a pre-calculus twelve question from the topic ”Solving Equations and Inequalities”. The correct choice is B.